CN111090904A - Soil pressure calculation method based on generalized double-shear stress yield criterion - Google Patents

Soil pressure calculation method based on generalized double-shear stress yield criterion Download PDF

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CN111090904A
CN111090904A CN201911337012.2A CN201911337012A CN111090904A CN 111090904 A CN111090904 A CN 111090904A CN 201911337012 A CN201911337012 A CN 201911337012A CN 111090904 A CN111090904 A CN 111090904A
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soil pressure
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CN111090904B (en
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苏丽娟
刘家顺
刘淼
贾宝新
付国胜
王云龙
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Liaoning Technical University
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Abstract

The invention provides a soil pressure calculation method based on a generalized double-shear stress yield criterion, and relates to the technical field of geotechnical engineering. The method is characterized in that firstly, based on a generalized double-shear stress criterion, a balance condition is established when any point in a soil body is in a limit balance state, and the generalized double-shear stress criterion considers two larger main shear stresses or a middle main stress sigma2And stress rod angle thetaσThe effect on yield or failure; meanwhile, the influence of hydrostatic pressure on yield or damage and the S-D effect of different tensile and compressive strengths of the material are also considered; then calculating the soil pressure distribution under the active limit state and the passive limit state based on the balance condition in the limit balance state; the method of the invention can provide a great result for the calculation of the active soil pressure, can provide early warning when the soil body does not reach the active limit state, can provide early warning when the calculation of the passive soil pressure is small, and can provide an early warning when the soil body does not reach the passive limit state, thereby being applied to engineeringAnd (4) reserving safely.

Description

Soil pressure calculation method based on generalized double-shear stress yield criterion
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a soil pressure calculation method based on a generalized double-shear stress yield criterion.
Background
In the design of retaining walls of projects such as side slopes, road beds, foundation pits and the like in geotechnical engineering, firstly, the calculation of soil pressure is required. The classical soil pressure calculation theory in the soil mechanics theory mainly includes Rankine (Rankine) and Coulomb (Coulomb) soil pressure theory, wherein the Rankine soil pressure theory is widely applied due to simple formula and clear meaning. The soil pressure theory is established based on the C-M yield criterion. The C-M yield criterion has simple form, easy parameter determination through experiments, convenience and practicability, thus being widely applied to geotechnical engineering. But the criterion fails to reflect the central principal stress (σ)2) The characteristics that yielding and damage are influenced and simple hydrostatic pressure can cause rock-soil yielding are provided, and other correction and improvement yielding criteria are proposed by a plurality of scholars later, for example, the scholars in China Shu Mao 37584c propose double-shear stress and generalized double-shear stress yielding and damage theories aiming at metal materials and rock-soil materials in 1961 and 1982.
The C-M yield criterion and the generalized double-shear stress criterion both belong to a shear stress yield theory, but the C-M criterion only considers the maximum shear stress during failure, and the generalized double-shear stress criterion considers two larger or middle principal stresses sigma2And stress Lode angle thetaσThe effect on yield or failure. The generalized double-shear stress criterion further considers the influence of hydrostatic pressure on yield or damage and considers the S-D effect of different tensile and compression strengths of the materials. Therefore, compared with a single shear stress criterion and other energy yield criteria, the method has obvious advantages and is more suitable for geotechnical materials.
In summary, it is necessary to provide a soil body extreme state calculation theory more suitable for rock-soil materials based on the generalized double shear stress yield criterion, so as to improve the existing active and passive soil pressure calculation methods.
Disclosure of Invention
The invention aims to solve the technical problem of providing a soil pressure calculation method based on the generalized double-shear stress yield criterion aiming at the defects of the prior art. The influence of two larger main shear stresses and hydrostatic pressure on soil yield damage is considered, a soil ultimate balance state calculation theory is established based on a generalized double-shear stress yield criterion, and soil pressure calculation of rock and soil materials is achieved.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a soil pressure calculation method based on a generalized double-shear stress yield criterion comprises the following steps:
step 1, establishing a balance condition when any point in a soil body is in a limit balance state based on a generalized double-shear stress yield criterion;
the soil body is an even and continuous semi-infinite space material, the surface of the soil body is horizontal, the microcell bodies at any point in the soil body are under the action of three-dimensional main stress, and the three-dimensional main stress is respectively as follows: the vertical stress being a major principal stress sigma1The horizontal stress is the central principal stress sigma2And small principal stress σ3；
The generalized double shear yield criterion is then expressed as:
when compressed in a broad sense: namely, it is
Figure BDA0002331203860000021
The method comprises the following steps:
Figure BDA0002331203860000022
when stretched in a broad sense: namely, it is
Figure BDA0002331203860000023
The method comprises the following steps:
Figure BDA0002331203860000024
wherein f is the yield function, τ23、τ13、τ12Respectively acting parallel to the principal stress sigma1、σ2、σ3Principal shear stress on the inclined plane of the shaft, σ12、σ23、σ13Respectively positive stress in a plane which is equi-inclined to the plane of the major axes of the microcells β, kbThe material constants are respectively the material constants of the generalized double-shear stress yield criterion and are determined by tests;
the strength of the generalized double-shear stress yield criterion and the C-M yield criterion is the same in uniaxial tension and uniaxial compression, and a material constant β, k of the generalized double-shear stress yield criterion is establishedbWith the material constant C of the C-M criterion,
Figure BDA0002331203860000025
the relationship between them is shown by the following formula:
Figure BDA0002331203860000026
Figure BDA0002331203860000027
wherein c is the cohesive force of the soil,
Figure BDA0002331203860000028
is the internal friction angle of the soil;
write the yield criterion of generalized double shear stress as
Figure BDA0002331203860000029
In the form of:
when in use
Figure BDA00023312038600000210
The method comprises the following steps:
Figure BDA00023312038600000211
when in use
Figure BDA00023312038600000212
The method comprises the following steps:
Figure BDA00023312038600000213
wherein, I1Is the stress full tensor first invariant of the microcell body, J2For stress deflection of a second invariant, θσIs the stress rod angle (i.e., Lode);
large principal stress sigma to the microcell bodies1Namely the dead weight stress of the soil at the point, the following formula is shown:
σ1＝γZ (4)
wherein gamma is the weight of the filling behind the wall, and Z is the distance between the calculation point and the surface of the filling;
assuming that the soil body is in a lateral limit condition, namely two horizontal stresses acting on the side surface of the microcell body are equal, then:
σ2＝σ3＝K0γZ (5)
wherein, K0The lateral pressure coefficient of the soil body;
Figure BDA0002331203860000031
due to the fact that
Figure BDA0002331203860000032
Therefore, it is
Figure BDA0002331203860000033
The compound represented by the formula (3a) is1Written in principal stress form:
Figure BDA0002331203860000034
order to
Figure BDA0002331203860000035
Figure BDA0002331203860000036
Substituting the formulas (5), (8) and (9) into the formula (6) for arrangement and simplification to obtain:
Figure BDA0002331203860000037
is obtained by the formula (6),
Figure BDA0002331203860000038
substituted into formula (10) to obtain:
Figure BDA0002331203860000039
Figure BDA00023312038600000310
the formulas (11) and (12) are balance conditions when one point in the soil body is in a limit balance state;
step 2, calculating the soil pressure distribution in the active limit state according to the balance condition in the limit balance state;
firstly, assuming that the soil mass in the range of a wedge behind a wall is in an active limit state, and the rest soil mass is in an elastic state; carrying out stress analysis on the wedge-shaped body; when the wall body has displacement in the direction deviating from the soil body, the soil body is gradually changed into an active state from the original static soil pressure state; at the moment, the vertical dead-weight stress borne by the soil body is a large main stress and a stress (sigma) with the same horizontal direction2＝σ3) Is a small principal stress; the small principal stress in the soil body is gradually reduced along with the increase of the displacement of the retaining wall until an active ultimate balance state is reached, and the large principal stress and the small principal stress meet the ultimate balance condition of the soil body;
the soil pressure in the active limit state in the soil body is the small principal stress as obtained by the formula (12):
Figure BDA0002331203860000041
wherein p isaIs the earth pressure in the active limit state, KaIs the soil pressure coefficient under the active limit state,
Figure BDA0002331203860000042
the earth pressure in the active limit state is composed of two parts, the first part, as obtained by the formula (13)
Figure BDA0002331203860000043
Generated by the self-weight of the soil and proportional to the depth Z, the part being in triangular distribution and the second part
Figure BDA0002331203860000044
Generated by cohesive force of cohesive soil, is independent of the depth Z, and is distributed in a rectangular shape; let the depth Z of equation (13) be zero, which is the cracking depth of the soil, as shown in the following equation:
Figure BDA0002331203860000045
step 3, calculating the soil pressure distribution in the passive limit state according to the balance condition in the limit balance state;
in the passive limit state, the soil pressure calculation formula in the soil passive limit state is obtained by the limit balance condition formula (11), and the following formula is shown:
Figure BDA0002331203860000046
wherein p ispFor passive earth pressure, KpIs the soil pressure coefficient in the passive limit state,
Figure BDA0002331203860000047
the soil pressure distribution under the passive limit state also comprises two parts, wherein the first part is
Figure BDA0002331203860000048
Is in direct proportion to the depth Z and is distributed in a triangular shape; the second part is
Figure BDA0002331203860000051
Generated by cohesive force of cohesive soil, is independent of depth and is distributed in a rectangular shape.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: compared with the result of the classical Rankine classical theory calculation, the improved soil pressure calculation method provided by the invention has the advantage that the precision is improved. The active soil pressure calculation result is large, early warning can be provided when the soil body does not reach the active limit state, the passive soil pressure calculation is small, and early warning can be provided when the soil body does not reach the passive limit state, so that certain safety reserve can be provided in engineering application, and the method has great advantages compared with a classical calculation formula. Meanwhile, the invention applies the generalized double-shear stress criterion to consider two larger main shear stresses or middle main stresses sigma2And stress rod angle (Lode) thetaσThe effect on yield or failure. The influence of hydrostatic pressure on yielding or damage is further considered according to the generalized double-shear stress criterion, the S-D effect of different tensile and compression strengths of the materials is considered, and the safety and the applicability of the design of the retaining wall are guaranteed.
Drawings
FIG. 1 is a schematic diagram of the stress distribution at any point in the soil mass according to the embodiment of the present invention;
fig. 2 is a schematic diagram of a soil pressure limit state in a limit state according to an embodiment of the present invention, wherein (a) is a schematic diagram of an active limit state, and (b) is a schematic diagram of a passive limit state;
fig. 3 is a soil pressure distribution diagram in a passive limit state according to an embodiment of the present invention, where (a) is the soil pressure distribution diagram in the active limit state, and (b) is the soil pressure distribution diagram in the passive limit state.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
A soil pressure calculation method based on a generalized double-shear stress yield criterion comprises the following steps:
step 1, establishing a balance condition when any point in a soil body is in a limit balance state based on a generalized double-shear stress yield criterion;
for the soil body is uniform and continuous semi-infinite space material, the surface of the soil body is horizontal, the microcell bodies at any point in the soil body are acted by three-dimensional main stress, as shown in figure 1, the three-dimensional main stress is respectively: the vertical stress being a major principal stress sigma1The horizontal stress is the central principal stress sigma2And small principal stress σ3；
The generalized double shear yield criterion is then expressed as:
when compressed in a broad sense: namely, it is
Figure BDA0002331203860000052
The method comprises the following steps:
Figure BDA0002331203860000053
when stretched in a broad sense: namely, it is
Figure BDA0002331203860000061
The method comprises the following steps:
Figure BDA0002331203860000062
wherein f is the yield function, τ23、τ13、τ12Respectively acting parallel to the principal stress sigma1、σ2、σ3Principal shear stress on the inclined plane of the shaft, σ12、σ23、σ13Respectively positive stress in a plane which is equi-inclined to the plane of the major axes of the microcells β, kbThe material constants are respectively the material constants of the generalized double-shear stress yield criterion and are determined by tests;
the strength of the generalized double-shear stress yield criterion and the C-M yield criterion is the same in uniaxial tension and uniaxial compression, and a material constant β, k of the generalized double-shear stress yield criterion is establishedbWith the material constant C of the C-M criterion,
Figure BDA0002331203860000063
the relationship between them is shown by the following formula:
Figure BDA0002331203860000064
Figure BDA0002331203860000065
wherein c is the cohesive force of the soil,
Figure BDA0002331203860000066
is the internal friction angle of the soil;
write the yield criterion of generalized double shear stress as
Figure BDA0002331203860000067
In the form of:
when in use
Figure BDA0002331203860000068
The method comprises the following steps:
Figure BDA0002331203860000069
when in use
Figure BDA00023312038600000610
The method comprises the following steps:
Figure BDA00023312038600000611
wherein, I1Is the stress full tensor first invariant of the microcell body, J2For stress deflection of a second invariant, θσIs the stress rod angle (i.e., Lode);
as can be seen from FIG. 1, the microcells are subjected to a large principal stress σ1Namely the dead weight stress of the soil at the point, the following formula is shown:
σ1＝γZ (4)
wherein gamma is the weight of the earth filled behind the wallThe bit is kN/m3Z is the distance (i.e., depth) of the calculated point from the surface of the fill in m;
assuming that the soil body is in a lateral limit condition, namely two horizontal stresses acting on the side surface of the microcell body are equal, then:
σ2＝σ3＝K0γZ (5)
wherein, K0The lateral pressure coefficient of the soil body;
Figure BDA0002331203860000071
due to the fact that
Figure BDA0002331203860000072
Therefore, it is
Figure BDA0002331203860000073
The compound represented by the formula (3a) is1Written in principal stress form:
Figure BDA0002331203860000074
order to
Figure BDA0002331203860000075
Figure BDA0002331203860000076
Substituting the formulas (5), (8) and (9) into the formula (6) for arrangement and simplification to obtain:
Figure BDA0002331203860000077
is obtained by the formula (6),
Figure BDA0002331203860000078
substituted into formula (10) to obtain:
Figure BDA0002331203860000079
Figure BDA00023312038600000710
the formulas (11) and (12) are balance conditions when one point in the soil body is in a limit balance state;
step 2, calculating the soil pressure distribution in the active limit state according to the balance condition in the limit balance state;
first, assume that the soil mass in the wedge-shaped range behind the wall is in an active limit state, and the rest of the soil mass is in an elastic state, as shown in fig. 2 (a). And carrying out stress analysis on the wedge-shaped body. When the wall body is displaced in the direction deviating from the soil body, the soil body is gradually changed into an active state from the original static soil pressure state. At the moment, the vertical dead-weight stress borne by the soil body is a large main stress and a stress (sigma) with the same horizontal direction2＝σ3) Is a small principal stress. The small principal stress in the soil body is gradually reduced along with the increase of the displacement of the retaining wall until an active ultimate balance state is reached, and the large principal stress and the small principal stress meet the ultimate balance condition of the soil body.
The soil pressure in the active limit state in the soil body is the small principal stress, which is obtained by the formula (12), and the following formula is shown:
Figure BDA0002331203860000081
wherein p isaThe soil pressure in the active limit state is expressed in kPa, KaIs the soil pressure coefficient under the active limit state,
Figure BDA0002331203860000082
the earth pressure in the active limit state is composed of two parts, the first part, as obtained by the formula (13)
Figure BDA0002331203860000083
Generated by the self-weight of the soil and is in direct proportion to the depth Z,the part is distributed in a triangular shape, and the second part
Figure BDA0002331203860000084
The portion generated by cohesive force of cohesive soil is rectangular regardless of the depth Z, as shown in fig. 3 (a); after the two parts of stress are superposed, a tension area and a compression area appear. In fact, the tensile strength of the soil body material is very small, and the soil body is separated from the wall body under the action of very small tensile force, so that the retaining wall is considered not to bear the tensile force, namely the actual soil pressure is only a triangular part; let the depth Z of equation (13) be zero, which is the cracking depth of the soil, as shown in the following equation:
Figure BDA0002331203860000085
step 3, calculating the soil pressure distribution in the passive limit state according to the balance condition in the limit balance state;
in the passive limit state, this is shown in fig. 2 (b). And (3) obtaining a soil pressure calculation formula under the soil passive limit state by the limit balance condition formula (11), wherein the formula is as follows:
Figure BDA0002331203860000086
wherein p ispIs passive earth pressure in kPa, KpIs the soil pressure coefficient in the passive limit state,
Figure BDA0002331203860000087
the soil pressure distribution under the passive limit state also comprises two parts, wherein the first part is
Figure BDA0002331203860000088
Is in direct proportion to the depth Z and is distributed in a triangular shape; the second part is
Figure BDA0002331203860000089
Generated by cohesive force of cohesive soil, is distributed in a rectangular shape regardless of the depth Z, as shown in FIG. 3(b), and has two partsThe partial stresses are superposed to obtain the soil pressure in a passive limit state, and the soil pressure is distributed in a trapezoidal shape.
Example 1:
in this embodiment, a retaining wall active earth pressure centrifugal model using Nanjing mica sand as a test material is taken as an example to perform a test and calculation of earth pressure in an active limit state; wherein, the height H of the model wall is 190mm, the centrifugal acceleration is 50g, and the geometric similarity ratio lambda of the model is 1: 100. Measuring the internal friction angle of the soil body according to a drainage shear test
Figure BDA0002331203860000091
γ＝12.6kN/m3The soil pressure at the active limit state of the measuring point was measured to be 45.26kPa at a burial depth of 130mm (calculated depth Z was 13m in terms of the model similarity ratio λ) by the test. P can be obtained by adopting the classical Rankine soil pressure calculation theorya＝tan2(45 ° - Φ/2) γ z 35.25kPa, using the improved soil pressure calculation method of the present invention:
Figure BDA0002331203860000092
compared with the classical soil pressure theory, the calculation result is closer to the test result.
Example 2:
in this embodiment, taking a retaining wall active earth pressure geotechnical centrifugal model with a model wall height H of 25cm as an example, the earth pressure under an active limit state is tested and calculated; the test soil body is cohesive soil, and the geometric similarity ratio lambda of the model is 1: 100. The shear strength index c of the soil body measured according to the large direct shear test is 38.2kPa,
Figure BDA0002331203860000093
γ＝18.6kN/m3the active soil pressure of the measuring point was 237.44kPa, and the buried depth was 240mm (calculated depth Z: 24m by conversion from the model similarity ratio lambda) was measured by the test. P can be obtained by adopting the classical Rankine soil pressure calculation theorya＝tan2(45 ° - Φ/2) γ z-2c tan (45 ° - Φ/2) ═ 146.94kPa, using the improved soil pressure calculation method of the present invention:
Figure BDA0002331203860000094
compared with the classical soil pressure theory, the calculation result is closer to the test result.
Example 3: in this example, a test material is sandy soil, and a large-scale retaining wall with a wall height H of 1.68m is taken as an example, and a soil pressure in a passive limit state is tested and calculated. The strength index c corresponding to the test soil is 14kPa,
Figure BDA0002331203860000095
γ＝18.6kN/m3the soil pressure under the passive limit state of the measuring point with the burial depth of 1.2m is 171.63kPa, and p can be obtained by adopting the classical Rankine soil pressure calculation theoryp＝tan2(45 ° + Φ/2) γ z +2c tan (45 ° + Φ/2) ═ 199.17kPa, using the improved soil pressure calculation method of the present invention:
Figure BDA0002331203860000096
compared with the classical soil pressure theory, the calculation result is closer to the test result.
Examples 1-3 the results of comparing the soil pressure obtained by the test and calculation and the calculation error are shown in table 1:
TABLE 1 soil pressure comparison results and calculation errors obtained by test and calculation
Figure BDA0002331203860000097
Figure BDA0002331203860000101
As can be seen from Table 1, compared with the result of the classical Rankine theory calculation, the improved soil pressure calculation method provided by the invention has the advantage that the precision is improved. The soil pressure under the active limit state is calculated to be larger, early warning can be provided when the soil body does not reach the active limit state, the soil pressure under the passive limit state is calculated to be smaller, and early warning can be provided when the soil body does not reach the passive limit state, so that certain safety reserve can be provided in engineering application, and the soil pressure early warning method has a larger advantage compared with a classical calculation formula.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (4)

1. A soil pressure calculation method based on a generalized double-shear stress yield criterion is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a balance condition when any point in a soil body is in a limit balance state based on a generalized double-shear stress yield criterion;
step 2, calculating the soil pressure distribution in the active limit state according to the balance condition in the limit balance state;
firstly, assuming that the soil mass in the range of a wedge behind a wall is in an active limit state, and the rest soil mass is in an elastic state; carrying out stress analysis on the wedge-shaped body; when the wall body has displacement in the direction deviating from the soil body, the soil body is gradually changed into an active state from the original static soil pressure state; at the moment, the vertical dead-weight stress borne by the soil body is a large main stress and a stress (sigma) with the same horizontal direction2＝σ3) Is a small principal stress; the small principal stress in the soil body is gradually reduced along with the increase of the displacement of the retaining wall until an active ultimate balance state is reached, and the large principal stress and the small principal stress meet the ultimate balance condition of the soil body;
and 3, calculating the soil pressure distribution in the passive limit state according to the balance condition in the limit balance state.
2. The soil pressure calculation method based on the generalized double-shear stress yield criterion as recited in claim 1, wherein: the specific method of the step 1 comprises the following steps:
the soil body is uniform and continuous semi-infinite space material, the surface of the soil body is horizontal, and the soil bodyThe micro-unit body at any point in the three-dimensional stress is acted by three-dimensional main stress, and the three-dimensional main stress is respectively as follows: the vertical stress being a major principal stress sigma1The horizontal stresses are a central principal stress sigma 2 and a small principal stress sigma3；
The generalized double shear yield criterion is then expressed as:
when compressed in a broad sense: namely, it is
Figure FDA0002331203850000011
The method comprises the following steps:
Figure FDA0002331203850000012
when stretched in a broad sense: namely, it is
Figure FDA0002331203850000013
The method comprises the following steps:
Figure FDA0002331203850000014
wherein f is the yield function, τ23、τ13、τ12Respectively acting parallel to the principal stress sigma1、σ2、σ3Principal shear stress on the inclined plane of the shaft, σ12、σ23、σ13Respectively positive stress in a plane which is equi-inclined to the plane of the major axes of the microcells β, kbThe material constants are respectively the material constants of the generalized double-shear stress yield criterion and are determined by tests;
the strength of the generalized double-shear stress yield criterion and the C-M yield criterion is the same in uniaxial tension and uniaxial compression, and a material constant β, k of the generalized double-shear stress yield criterion is establishedbWith the material constant C of the C-M criterion,
Figure FDA0002331203850000015
the relationship between them is shown by the following formula:
Figure FDA0002331203850000016
Figure FDA0002331203850000021
wherein c is the cohesive force of the soil,
Figure FDA0002331203850000022
is the internal friction angle of the soil;
write the yield criterion of generalized double shear stress as
Figure FDA0002331203850000023
In the form of:
when in use
Figure FDA0002331203850000024
The method comprises the following steps:
Figure FDA0002331203850000025
when in use
Figure FDA0002331203850000026
The method comprises the following steps:
Figure FDA0002331203850000027
wherein, I1Is the stress full tensor first invariant of the microcell body, J2For stress deflection of a second invariant, θσIs the stress rod angle (i.e., Lode);
large principal stress sigma to the microcell bodies1Namely the dead weight stress of the soil at the point, the following formula is shown:
σ1＝γZ (4)
wherein gamma is the weight of the filling behind the wall, and Z is the distance between the calculation point and the surface of the filling;
assuming that the soil body is in a lateral limit condition, namely two horizontal stresses acting on the side surface of the microcell body are equal, then:
σ2＝σ3＝K0γZ (5)
wherein, K0The lateral pressure coefficient of the soil body;
Figure FDA0002331203850000028
due to the fact that
Figure FDA0002331203850000029
Therefore, it is
Figure FDA00023312038500000210
The compound represented by the formula (3a) is1Written in principal stress form:
Figure FDA00023312038500000211
order to
Figure FDA0002331203850000031
Figure FDA0002331203850000032
Substituting the formulas (5), (8) and (9) into the formula (6) for arrangement and simplification to obtain:
Figure FDA0002331203850000033
is obtained by the formula (6),
Figure FDA0002331203850000034
substituted into formula (10) to obtain:
Figure FDA0002331203850000035
Figure FDA0002331203850000036
equations (11) and (12) are the equilibrium conditions when one point in the soil body is in the limit equilibrium state.
3. The soil pressure calculation method based on the generalized double-shear stress yield criterion as recited in claim 2, wherein: according to the equilibrium condition formula (12) in the extreme equilibrium state, the soil pressure in the active extreme state in the soil mass calculated in the step 2 is the small principal stress, and the following formula is shown:
Figure FDA0002331203850000037
wherein p isaIs the earth pressure in the active limit state, KaIs the soil pressure coefficient under the active limit state,
Figure FDA0002331203850000038
the earth pressure in the active limit state is composed of two parts, the first part, as obtained by the formula (13)
Figure FDA0002331203850000039
Generated by the self-weight of the soil and proportional to the depth Z, the part being in triangular distribution and the second part
Figure FDA00023312038500000310
Generated by cohesive force of cohesive soil, is independent of the depth Z, and is distributed in a rectangular shape; let the depth Z of equation (13) be zero, which is the cracking depth of the soil, as shown in the following equation:
Figure FDA0002331203850000041
4. the soil pressure calculation method based on the generalized double-shear stress yield criterion as recited in claim 2, wherein: according to the equilibrium condition formula (11) in the limit equilibrium state, the soil pressure in the passive limit state of the soil body calculated in the step 3 is shown as the following formula:
Figure FDA0002331203850000042
wherein p ispFor passive earth pressure, KpIs the soil pressure coefficient in the passive limit state,
Figure FDA0002331203850000043
the soil pressure distribution under the passive limit state also comprises two parts, wherein the first part is
Figure FDA0002331203850000044
Is in direct proportion to the depth Z and is distributed in a triangular shape; the second part is
Figure FDA0002331203850000045
Generated by cohesive force of cohesive soil, is independent of depth and is distributed in a rectangular shape.
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